Nouvelle famille de solutions approchées pour certaines équations de Schrödinger non séparables. Application à l'état fondamental de l'hélium

Abstract

Un mode de formation de solutions approximatives de l'équation de Schrödinger des atomes à deux électrons est exploité systématiquement. Il mène à des fonctions d'onde pourvues de propriétés qui les rapprochent beaucoup de la solution rigoureuse. En les prenant comme fonctions d'essai dans un calcul de variations on détermine la valeur propre de l'état fondamental de l'hélium à I,3 pour I000 près et le potentiel d'ionisation à 4,5 pour I000 près. L'intérêt de la méthode est qu'elle semble bien s'appliquer quand la théorie ordinaire des perturbations ne donne pas de bons résultats

Electron correlations in single-electron capture from helium by fast protons andαparticles

“…As can be expected, at lower energies, the CB1-4B cross sections are much smaller than the corresponding results of the CDW-4B model. A comparison is also made with the continuum-distortedwave-independent-event model (CDW-IEM) of Dunseath and Crothers [54], derived using the correlated Pluvinage wave function [55] ϕ i ( x 1 , x 2 ) = (Z 3 T /π ) exp[−Z T (x 1 + x 2 )] exp(−ikr 12 ) 1 F 1 (1 − iγ, 2, 2ikr 12 ), where γ = −1/(2k) and c(k) is the normalization constant, with k being a nonlinear variational parameter. This wave function contains two entirely uncorrelated hydrogenlike wave functions with the unscreened charge Z T that are multiplied with a corrective r 12 -dependent term of the form exp(−ikr 12 ) 1 F 1 (1 − iγ, 2, 2ikr 12 ).…”

Analysis, by the Monte Carlo method, of the validity of the diffusion approximation in a study of dynamic multiple scattering of light in randomly inhomogeneous media

“…The initial state, which consists of the incident electron and the bound electrons, will be the product of a plane wave describing the incident electron and a correlated Pluvinage type wavefunction (Pluvinage 1951) describing the two bound ones:…”

“…The underlying mathematical approach in the determination of correlated wavefunction φ i (r 1 , r 2 ) is the concept of semi-separability of the Schrödinger equation, following Pluvinage (1951), where φ i (r 1 , r 2 ), has an explicit dependence on the interelectronic distance r 12 . For some special potentials, V 1 , V 2 and V 12 , the Schrödinger equation is said to be semi-separable if one can solve exactly the two equations below:…”

On the use of analytic ansatz three–body wave functions in the study of (e, 2e) band related processes

“…They assumed that the three-body wave function could be approximated by three two-body subsystems, each acting independently of the other. This idea is based upon one first formulated by Pluvinage (1950Pluvinage ( , 1951 and later used by Garibotti & Miraglia (1980) and Godunov et al . (1983).…”